Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in PYTHON3):

Solution:
# -*- coding: utf-8 -*-
'import sys'
'import math'
n=int(input())
A=[int(i) for i in input().split()]
A.sort()
ans=0.0
for i in range(1,n):
    cd = int(A[i])-int(A[i-1])
    if i==n-1: 
        ab=int(A[n-3])+int(A[n-4])
    elif i==n-2: 
        ab=int(A[n-1])+int(A[n-4])
    else:
         ab=int(A[n-1])+int(A[n-2])
    ans=max(ans,ab/cd)
print(ans)